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Japan Stock Index

Calculation Method

The Nikkei Stock Average is the average price of 225 stocks traded on the first section of the Tokyo Stock Exchange, but it is different from a simple average in that the divisor is adjusted to maintain continuity and reduce the effect of external factors not directly related to the market.

Equation

Nikkei Average = Sum of stock prices of 225 constitutents

Divisor
a) Stocks that do not have a par value of 50 yen are converted to 50 yen par value.
b) Numbers are rounded to two digits after the decimal point, or hundredths, to calculate the average.
c) Priority in the usage of prices are:

1. Current special quotation (closing special quotation).
2. Current price (closing price).
3. Standard price, which is defined as follows:

The theoretical price of ex-rights, a special quotation from the previous day or the closing price from the previous day, in this order of priority.

Adjustment of divisors

When components change or when they are affected by changes outside of the market, the divisor is adjusted to keep the index level consistent.

1) In the case of ex-rights

New Divisor = Old Divisor X(sum of stock prices cum rights – sum of rights prices)

sum of stock prices cum rights
Rights prices = last cum stock price theoretical value of ex-rights
Theoretical value of ex-rights = last cum stock price+paid-in amount X paid-in allotment ratio

paid-in allotment ratio + split allotment ratio

When there is no split or a reverse split, the split-allotment ratio shall be one.

2) In case of capital decrease

Theoretical value of ex-rights = last cum stock price

1-ratio of capital decrease

3) In the case of replacement of components in the average

Rights price = price of replaced components – price of added components

4) In the case of stock buyback by issuer

Divisor not adjusted

Magnifications

Adjusted magnification = 225

divisor
Adjusted magnification = Adjusted average = sum of stock prices / sum of stock prices = 225




mathematical average divisor 225 divisor

 

April 2000 Revision

The concepts of “Periodic Review” and “Extraordinary Review” were redefined, and timing for the reviews was changed. The primary purpose of the Periodic Review is to annually reconsider component issues from the standpoint of changes in the industrial and market structures. The Extraordinary Review is for deleting and adding components in response to extraordinary developments, such as bankruptcies or mergers.

Periodic Review Standards

In principle, the Periodic Review shall be conducted annually in October in line with the rules in place. The Periodic Review may, however, be carried out more than once a year if necessary.

Active Approach To Deletions/Additions

The most important changes is that the Periodic Review process is carried out in a far more comprehensive and dynamic manner. The rules previously required replacement of an issue if liquidity had declined significantly, or if a company was delisted.

The revised rules call for a more active approach to deletions and additions by requiring consideration of changes in the industrial structure and market environment, in addition to liquidity. In view of the desire for a more dynamic review process, no limit is placed on the number of issues that can be replaced.

Assessing Liquidity

While the principle of favoring highly liquid stocks was maintained, the yardstick for assessing liquidity was revised. The former measures of “Trading Volume” and “Price Fluctuation to Volume” were replaced by “Trading Value” and “Rate of Price Fluctuation to Volume.”

The new measures are seen as better gauges of liquidity because they combine Trading Value, a standard for measuring turnover, and Rate of Price Fluctuation to Trading Volume, which is important in view of the increase in the number of high-priced issues.

Trading Value is calculated by multiplying the average of four prices (open, high, low and close) by number of shares traded. The period over which liquidity is measured was shortened to five years, from 10. The primary reason for this is to track changes in the market as closely as possible while eliminating the impact of factors that temporarily increase liquidity in the market.

Selection of Highly Liquid Stocks

The practice of assigning highly liquid stocks to the “High-liquidity Group” has not changed. Formerly, all stocks on the first section of the Tokyo Stock Exchange were ranked in order of liquidity and the top 50% were considered high-liquidity issues. This approach has been replaced with one in which the 450 most liquid issues are chosen (a figure double the 225 component stocks of the index).

The approach of selecting the top 50% was abandoned because the number of issues listed on the first section of the TSE is growing and there was concern that the method would not result in a list representative of highly liquid issues. A predetermined figure that limits the population to a number double the component count was considered to be more practical and reasonable.

Mandatory Deletion/Addition

The rule mandating deletion of issues that fall outside the high-liquidity group remains unchanged. Since the high-liquidity group is now limited to 450 stocks, all issues ranked 451 and below are automatically excluded.

Another important change involves elimination of the rule stating that only six issues could be removed from the index in a single review period. This was replaced by a rule requiring that the 75 most liquid issues (one-third of the component count of the Nikkei average) be included in the index.

Deletion/Addition Based on Sector Balance

A new concept based on six industrial sectors was adopted with these revisions. This was accomplished by consolidating Nikkei’s 36 industrial categories into six: Technology, Financials, Consumer Goods, Materials, Capital Goods/Others, and Transportation/Utilities. Component stocks of the Nikkei average are balanced among these six sectors.

Choice of the sector approach reflects a belief that actively rebalancing component stocks from a broader perspective is required to accurately represent dynamic changes in the industrial structure. Procedures for inter-sector rebalancing are as follows.

(a) The 450 high-liquidity issues are classified into the six sector categories. Half of the number of issues in each sector will be considered the “Appropriate Number of Issues” for that sector to be included in the index. This percentage reflects the fact that the number 450 is double the number of Nikkei average components.

(b) The Mandatory Deletion / Addition rule is applied to the Appropriate Number of Issues to show if too many or too few have been chosen. For example, if the number of issues appropriate for a sector is 30 and the actual number of issues obtained after applying the rule is only 28, then two issues will be added to bring the sector’s count to 30.

Adjustments will be made for excesses or shortages in each sector as follows. If the number of companies for a specific sector in the top 75 most liquid issues that will be automatically included in the 225 components excesses in the Appropriate number of Issues for a sector, the excess is ignored and all issues are initially included.

(c) The excess in a sector resulting from automatic inclusion as described above is adjusted by removing an equivalent number of issues from the sector, starting with the issue exhibiting the lowest level of liquidity.

(d) Shortage will be filled up by adding an equivalent number of issues from among companies currently excluded, starting with the issue exhibiting the highest level of liquidity.

This sector-based breakdown and the underlying industry classifications may be modified to reflect changes in the industrial structure. The 36 Nikkei industrial classifications included in the six sector categories are as follows:

Technology — Pharmaceuticals, Electrical Machinery, Automobiles, Precision Machinery, Telecommunications

Financials — Banks, Miscellaneous Finance, Securities, Insurance

Consumer Goods — Marine products, Food, Retail, Services

Materials — Mining, Textiles, Paper & Pulp, Chemicals, Oil, Rubber, Ceramics, Steel, Nonferrous metals, Trading House

Capital Goods/Others — Construction, Machinery, Shipbuilding, Transportation Equipment, Miscellaneous Manufacturing, Real estate

Transportation and Utilities — Railroads & Buses, Trucking, Shipping, Airlines, Warehousing, Electric Power, Gas.

Extraordinary Deletion

Basically, the rule requiring that a component stock be deleted when it is removed from the first section of the TSE (that is moved to the Liquidation post known as “Seiri Post”), delisted due to a merger or insolvency (insolvency is assumed when a company files for protection from creditors) or singled out for some other extraordinary reason has not been changed.

A component stock moved to “Kanri Post” (Post for stocks under supervision) is in principle a candidate for deletion.

Stocks are moved to Kanri Post for a variety of reasons, including likely delisting or during a temporary period of investigation and monitoring. In such cases, the decision to delete a stock from the average will depend on circumstances particular to the issue in question.

If one or more component stocks is deleted from the average, the schedule for filling the resulting opening is as follows:
(1) The “Shortage Ratio” was used previously for choosing the issue to replace a deleted component, with priority given to the most underrepresented industrial classifications. The new Periodic Review system focuses on the sector with the vacancy and requires selection of the stock with the highest liquidity among sector issues that have not been included in the average in the past. Given one deletion in financials, a newly-selected issue will come from financials.

(2) As a rule, replacement will be effective on the day an opening emerges. If a component is moved to Seiri Post, the change goes into effect on the day the issue is moved.

If a vacancy develops suddenly on a day the market is closed, a certain interim period may be allowed before the opening is filled, to announce the date and details of replacement ahead of time. This rule is used in cases where a company files for protection under the Corporate Reorganization Law at night or on a public holiday.

Other Revisions

The rules under “Exceptions to Addition Policy” and “Special Additions” have been abolished. Exceptions to Addition Policy rules stated that companies qualifying for an exceptional addition had to be listed on the first section of the TSE for more than 3 years and have a float exceeding 6 million shares. Special Additions rule stated that a firm considered representative of its industry by TSE would be included.

Some companies may be delisted as they move forward with restructuring or diversification programs. In such cases, component issues will be replaced in accordance with the following procedures, depending upon the nature of the reorganization.

Replacement procedures will not be implemented immediately but held pending until the next Periodic Review so that liquidity can be monitored around the time of the reorganization and the new entity’s status measured in terms of its being representative of its industry. This means that the delisting process will be handled as before.

It should also be noted that in the following cases, the issue may not necessarily be included at the next Periodic Review.

(1) If a non-component issue becomes the surviving entity in a merger between TSE first section companies, and the current component issue is the company absorbed by the surviving entity, the surviving non-component issue may be included in the index.

(2) When a component issue is delisted following the formation of a holding company (including formation of a holding company by several listed firms), the newly established “Holding Company” may be included as an index component.

Revisions to the Nikkei Indices Selection Rules 2002

Nikkei Inc. revised the component selection rules for the Nikkei Stock Average (Nikkei Average or Nikkei 225), Nikkei Stock Index 300 and Nikkei 500 Stock Average from February 1, 2002.

The previous rule stipulated that the constituents were to be removed and added immediately after corporate failure events. When constituents filed for bankruptcy or were moved to Seiri-Post by the Tokyo Stock Exchange, changes to the indices were made after the close of the same day.

However, in the face of recent economic conditions, to enable the users respond to the changes smoothly and to make the changes better known to the public, new constituents are added after an interval under the revised rules.

The interval is approximately two days and the exact number of days will be announced at each event. Constituents which are moved to Seiri-Post continue to be removed on the day of the event. The Nikkei Average will be calculated with fewer than 225 constituents before the addition of new components.